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We apply results of Malliavin-Thalmaier-Watanabe for strong and weak Taylorexpansions of solutions of perturbed stochastic differential equations (SDEs).In particular, we work out weight expressions for the Taylor coefficients ofthe expansion. The results are applied to LIBOR market models in order to dealwith the typical stochastic drift and with stochastic volatility. In contrastto other accurate methods like numerical schemes for the full SDE, we obtaineasily tractable expressions for accurate pricing. In particular, we present aneasily tractable alternative to ``freezing the drift'' in LIBOR market models,which has an accuracy similar to the full numerical scheme. Numerical examplesunderline the results.

Weak and Strong Taylor methods for numerical solutions of stochastic differential equations